1. Field of the Invention
The present invention relates to a vibrating element capable of vibrating under an expansion mode and, more particularly, to a piezoelectric vibrator defined by a thin piezoelectric film deposited on a substrate made of a constant modulus alloy and a vibration electrode film deposited on the piezoelectric film.
2. Description of the Prior Art
Piezoelectric vibrators of the above described type generally have a circular or square configuration. In such a case, the relationship between the vibration frequency F0 and the expanding direction length A, which is equal to the diameter of the vibrator when it is circular, or is equal to one side of the vibrator when it is square, can be given as follows: ##EQU1## wherein C is a constant as follows, ##EQU2## P is Poisson's ratio, E is Young's modulus, D is density and A is the distance between opposite edges of the vibrator for determining the vibration frequency. As is apparent from the above equation, the size of the vibrating element becomes smaller as the vibration frequency increases. Thus, when a vibrating element that vibrates at a high frequency is required, it is very difficult to handle the element, because its size is very small.